Terahertz (THz) technologies utilize electromagnetic radiation generally in the frequency range between 100 GHz and 10 THz (i.e., wavelengths of 3 mm to 30 μm, energies of 0.4 to 40 meV, or equivalent blackbody radiation temperatures of 5 K to 500 K). Many non-metallic materials that are visually opaque are partially transparent or exhibit molecular resonances in the terahertz region. Therefore, terahertz technologies have many potential applications in diverse fields, including molecular spectroscopy, space and atmospheric sciences, plasma physics, biology, medical imaging, remote sensing, and communications. In particular, the terahertz region of the electromagnetic spectrum offers considerable promise for covert communications, spectroscopic imaging of illicit and hazardous materials, and chemical and biological sensing. See B. Ferguson and X-C Zhang, Nature Materials 1, 26 (2002).
However, lying in the “terahertz gap” between the infrared and microwave regions of the electromagnetic spectrum, terahertz technologies have not been adequately developed to meet the requirements of many of the potential applications. Passive and active devices operating at terahertz frequencies are currently a challenge, and a promising emerging technology for such devices is optical metamaterials. Metamaterials are artificially structured materials in which both the electric permittivity E and the magnetic permeability μ are tunable. Such materials can possess a negative index of refraction and are sometimes referred to as “left-handed,” when the wave vector is antiparallel to the usual right-handed cross product of the electric and magnetic fields characteristic of naturally occurring materials. Metamaterials have electromagnetic properties that are difficult or impossible to achieve with conventional right-handed materials, the most notable being the negative refractivity. These unconventional properties suggest a number of unique applications, including compact aberration-free lenses, subwavelength imaging, and cloaking. However, although materials with negative electric permittivity are readily available at low frequencies, including metals below the ultraviolet region and doped semiconductors in the terahertz and infrared regions, existing materials with negative magnetic permeability typically lose their magnetic activity at much lower frequencies. Therefore, until recently, artificial metamaterials having both negative permittivity and negative permeability in the same frequency range were difficult to realize in practice.
However, in the late 90s, Pendry proposed a practical split-ring resonator (SRR) structure that can be used to achieve a negative permeability in the vicinity of a magnetic resonance frequency. See J. B. Pendry et al. IEEE Trans. Microwave Theory Tech. 47, 2075 (1999). When combined with continuous wires, one can simultaneously obtain a negative permittivity and a negative permeability, thereby exhibiting a left-handed index of refraction. See D. R. Smith et al., Phys. Rev. Lett 84(19), 4184 (2000). As shown in FIG. 1, the simplest form of the SRR 10 is planar metallic ring 11 with a gap 12. The ring 11 has an outer dimension l and a metal linewidth w. The gap 12 has a width g. In essence, the SRR 10 is a small LC circuit consisting of an inductance L and a capacitance C. The ring 11 forms one winding of a coil (the inductance), and the ends form the plates of a capacitor. Electromagnetic radiation directed into the plane of the SRR induces a ring current i in the ring. Metamaterials comprise an array of such subwavelength metallic resonator structures within or on an electrically insulating or semiconducting substrate. Dense packing of SRRs, using lattice constants smaller than the LC resonance wavelength, creates a metamaterial that can exhibit a magnetic and electric resonance at the resonant frequency ωLC=1/√{square root over (LC)}. Two resonances are observed when exciting the SRR structure shown with incident radiation having polarization perpendicular to the gap (i.e., electric field E parallel to the arm containing the gap, as shown). The LC resonance corresponding to the ring current leads to a magnetic dipole moment perpendicular to the SRR plane and an electric dipole moment parallel to the incident electric field. A shorter wavelength Mie resonance is also excited, corresponding to an electric dipole oscillating in the arm opposite the gap. With incident radiation polarized parallel to the gap, only a Mie resonance corresponding to electric dipoles oscillating in the two arms parallel to the gap is observed. The resonances can be strengthened by adding additional, concentric rings, each ring having a gap, to the simple SRR structure. Other resonant structures can also be designed and implemented.
In addition, the resonator response is scalable from radio to optical frequencies. See D. R. Smith et al., Phys. Rev. Lett. 84, 4184 (2000); J. B. Pendry et al., Science 312, 1780 (2006); R. A. Shelby et al., Science 292, 77 (2001); and C. Enkrich et al., Phys. Rev. Lett. 95, 203901 (2005). For the simple SRR described above, both the inductance and capacitance scale proportionally to SRR size, provided that all SRR dimensions are scaled down simultaneously and that the metal retains a high conductivity. Therefore, the resonant frequency scales inversely with a normalized size (or scale factor, S), according to ωLC∝1/s. Therefore, metamaterials have the potential to provide a scale-invariant design paradigm to create functional materials which can enhance our ability to manipulate, control, and detect electromagnetic radiation. The recent growth in the field of metamaterials is partly due to the promise of new devices that exploit these novel electromagnetic properties in all frequency ranges, including terahertz. See B. Ferguson and X-C Zhang, Nature Materials 1, 26 (2002); M. C. K. Witshire et al., Science 291, 849 (2001); T. J. Yen et al., Science 303, 1494 (2004); and W. J. Padilla et al., Phys. Rev. Lett. 96, 107401 (2006).
However, such resonant structures can have losses which limit their performance, some of which are radiation losses and dielectric losses due to the substrate. Reducing dielectric losses in THz metamaterials would allow for improved terahertz devices that could be used in some of these applications. In addition, most metamaterial structures are planar and, therefore, highly anisotropic. Some of these device applications require the fabrication of three-dimensional (3D) metamaterials. However, fabricating 3D metamaterials is a challenge at terahertz and shorter wavelengths due to fabrication constraints.
Therefore, a need remains for microfabricated metamaterials that exhibit lower losses and that can be assembled into three-dimensional structures that enable full coupling of incident electromagnetic terahertz radiation in two or three orthogonal directions. Furthermore, due to the limited technology available for manipulation and control of terahertz radiation, there is a need for polarization sensitive and insensitive metamaterials at these frequencies that can enable new devices and applications. The ability to detect and control terahertz polarization with metamaterials would enable novel terahertz polarimetric devices.